MinT - Best Known (154, 200, s)-Nets in Base 3

Best Known (154, 200, s)-Nets in Base 3

(154, 200, 600)-Net over F₃ — Constructive and digital

Digital (154, 200, 600)-net over F₃, using

trace code for nets [i] based on digital (4, 50, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(154, 200, 1185)-Net over F₃ — Digital

Digital (154, 200, 1185)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 200, 66398)-Net in Base 3 — Upper bound on s

There is no (154, 200, 66399)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 265640 696959 551734 988639 133672 410929 873132 009657 431400 816484 995971 242215 717196 683223 765577 775955 > 3²⁰⁰ [i]